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Journal Articles Annals of Pure and Applied Logic Year : 2016

Polytopes and simplexes in p-adic fields

Abstract

We introduce topological notions of polytopes and simplexes, the latter being expected to play in p-adically closed fields the role played by real simplexes in the classical results of triangulation of semi-algebraic sets over real closed fields. We prove that the faces of every p-adic polytope are polytopes and that they form a rooted tree with respect to specialisation. Simplexes are then defined as polytopes whose faces tree is a chain. Our main result is a construction allowing to divide every p-adic polytope in a complex of p-adic simplexes with prescribed faces and shapes.
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Dates and versions

hal-01276748 , version 1 (10-03-2016)
hal-01276748 , version 2 (22-10-2016)

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Luck Darnière. Polytopes and simplexes in p-adic fields. Annals of Pure and Applied Logic, 2016, 168 (6), pp.1284-1307. ⟨hal-01276748v2⟩
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